It is known to replace damaged intervertebral discs with prostheses which consist of two cover plates, each to be connected to an adjacent vertebral body, and of a prosthesis core, said prosthesis core cooperating with one or both cover plates via complementary spherical surfaces of articulation (EP-B 298 233). The cover plates have contact surfaces by means of which they are connected to the adjacent vertebral bodies. It is desired that the centre of articulation of the prostheses be arranged in such a way that the movements permitted by the prosthesis are as far as possible identical to the natural ones and that forces can be transmitted uniformly between the vertebral bodies and the prosthesis. In known prostheses, this objective is approached by arranging the centre of articulation in a predetermined spatial relationship to the contact surfaces of the cover plates and by providing the cover plates with an edge which bears on the ventral margin of the associated vertebral body and thereby determines the relative position of the cover plate to the vertebral body (EP-B 560 140), or by using an implantation instrument which has a limit stop on the vertebral body (EP-B 333 990). This ensures an at all times identical position of the centre of articulation of the prosthesis in relation to the ventral edge of the vertebral bodies. It is also known (EP-A 955 021), in a system of intervertebral disc prostheses including several categories of different sizes, to provide corrective prostheses which belong on one side to one size category and on the other side to another size category.